The instant invention pertains generally to non-binary methods of computing and more particularly to methods for addition, subtraction, multiplication and division that utilize the digital multistate properties of phase change materials.
The development of the computer is commonly regarded as one of the most significant advances of the last half of the twentieth century. Computers have simplified many aspects of everyday life and have led to significant productivity gains in the economy. Recent needs in image processing and complex computing have spurned significant advances in microprocessor speed and memory storage density. Further advances and future applications of computers depend on mankind""s ability to process larger amounts of information in increasingly more efficient ways.
Silicon is at the heart of today""s computer. The advances in computing power and speed have largely been a consequence of better understanding the fundamental properties of silicon and harnessing those properties for practical effect. Initial progress was predicated on building basic electronic components such as transistors and diodes out of silicon and later progress followed from the development of integrated circuits. Recent advances represent a continuation of these trends and currently emphasize miniaturization and the integration of an ever larger number of microelectronic devices on a single chip. Smaller devices lead to higher memory storage densities, more highly integrated circuits and reduced interaction times between devices on the same chip.
The current strategy for improving processing speed and storage density depends on an ability to continue to miniaturize silicon based microelectronic devices. To date, miniaturization has approximately followed Moore""s Law. According to Moore""s Law, the number of transistors that can be integrated on a chip of a given size is expected to double every 18 months. Moore""s Law has proven to be a remarkably reliable predictor of progress over the last 25 years and we are currently at the point where chips contain tens of millions of transistors, each of which measures about 0.2 micron across.
The question for the future is whether miniaturization efforts can continue indefinitely or whether practical or fundamental physical limits will present insurmountable barriers to miniaturization. Significant practical limitations include crosstalk between devices on a chip and difficulties in further reducing the size of devices. Crosstalk corresponds to the leakage of current or charge from one device to neighboring devices. Ideally, all devices on a chip interact along predetermined interconnects defined by the logic or ultimately intended purpose of the chip. As miniaturization proceeds, however, the spaces between devices necessarily decreases and undesired interactions between devices becomes increasingly problematic as electric fields, charge or current from one device affect other devices by virtue of close spatial proximity rather than through patterned interconnects. Crosstalk interferes with the intended function of a chip.
The size of microelectronic devices that can be assembled on a chip is primarily a function of the lithography process used to pattern the devices. Lithography is a process of exposing a photoresist material to light. The dimensions of the photoresist material exposed to light are directly related to the dimensions of the ultimate devices formed on the chip. The wavelength of light used in lithography controls the dimensions of the photoresist material exposed to light. The shorter the wavelength of light used, the higher the resolution of the lithography process and the smaller the dimensions of the ultimate devices formed.
In principle, the practical limitations represented by crosstalk and lithographic resolution can be overcome. Crosstalk, for example, may be overcome by incorporating insulating layers with lower dielectric constants than are currently used in the transistor structure. Lithographic resolution can be improved by developing shorter wavelength light sources such as, for example, the excimer laser. Although these solutions, and others that have been proposed, are potentially possible; they are accompanied by tremendous increases in production costs. The cost of building a chip manufacturing facility has increased from less than $5 million to more than $1.5 billion over the past 25 years. Costs are expected to continue to escalate rapidly in the future and are currently becoming sufficiently severe that further improvements in chips may no longer be economically justifiable. The computer industry is at a crossroads.
In order for the computer industry to expand and for the computer to become more than a commodity item, revolutionary changes are needed in the way computers work and in the materials used in the processing and memory elements. Improvements in computing speed and efficiency as well as greater parallelness are among the advances needed if the conventional computer is to evolve toward a more interactive and adaptable learning machine.
The instant invention provides methods of computing in a non-binary fashion that utilize the digital multistate properties of a phase change material. The digital multistate phase change material may be incorporated into memory elements or registers of computers and other data processing units that are capable of implementing the instant computing methods. The digital multistate phase change memory materials utilized by the instant computing methods have at least a high resistance state and a detectably distinct low resistance state. Methods and algorithms for resetting memory elements comprised of a digital multistate phase change material, defining programming states for the storage of numbers, moving the contents of one memory element to another memory element, computing the complement of a number, and executing the mathematical operations of addition, subtraction, multiplication and division using a digital multistate phase change material are disclosed herein.
Memory elements comprising a digital multistate phase change material may be organized into memory groups where each memory element within a group may be used to store one digit of a multidigit number. A memory element shall also be referred to herein as a register. A memory group thus corresponds to a collection of memory elements or registers. The number of memory elements or registers included in a memory group is variable and is generally determined by the maximum number of digits that one wishes to associate with numbers for the purposes of storage. The maximum number of digits that one associates with a number represents a tradeoff between precision and efficiency of manipulation.
Through the grouping of registers to form memory groups, the memory elements may be programmed to store multidigit numbers. Instead of being limited to operations based on a binary or base 2 arithmetic system, the digital multistate characteristic of the phase change material permits the storage and processing of digits associated with any arithmetic base in the registers to achieve non-binary computational capability. Direct storage and processing of numbers in base 10, base 8, or base 16, for example, is possible with the instant invention. Bases of hundreds, thousands or even higher are also compatible with the instant invention. As a result, the instant invention provides an opportunity to achieve massively parallel computation. The parallel computation capability, higher storage densities and non-binary operation possible with multistate memory elements through the instant computing methods provide an opportunity to vastly improve the speed and efficiency of computation relative to conventional computing machines.
Algorithms disclosed herein describe methods for storing and processing information using multistate memory elements comprising a phase change material. Included in the instant invention are methods directed at single register operation as well as register by register operations of multistate memory groups. In these methods, energy is applied to a single register or to individual registers within a memory group to store a digit or to alter the value of a digit that has previously been stored. These methods include provisions for addressing individual registers and provide methodologies for manipulating a group of registers, or relevant subset thereof, associated with one or more memory groups to achieve a desired mathematical operation or processing objective.